Mixed Problem for a Linear Barenblatt–Zheltov–Kochina Equation with Fractional Hilfer Operator

The problems of single-valued regular solvability and the construction of the solution of a mixed problem for linear differential equations that contain the fractional analog of the Barenblatt–Zheltov–Kochina operator are studied. The method of a Fourier series based on the separation of variables is used. A countable system of linear integral equations with Hilfer fractional operator is obtained. Sufficient coefficient conditions for the unique regular solvability of the mixed problem are established. The method of successive approximations combined with the method of compressing mapping are applied.